Example Question #1 : Linear Motion

Marcus throws a ball directly up in the air with an initial velocity of . How high will the ball go?

Possible Answers:

Correct answer:

Explanation:

Remember that the final velocity at an object's highest point is equal to zero. We can use the following equation to solve for our height (), using the initial velocity, final velocity, and acceleration due to gravity.

Example Question #5 : Motion And Mechanics

A ball is thrown vertically with a velocity of . What is its velocity at the highest point in the throw?

Possible Answers:

There is insufficient information to solve

Correct answer:

Explanation:

When examining vertical motion, the vertical velocity will always be zero at the highest point. At this point, the acceleration from gravity is working to change the motion of the ball from positive (upward) to negative (downward). This change is represented by the x-axis on a velocity versus time graph. As the ball changes direction, its velocity crosses the x-axis, momentarily becoming zero.

Example Question #1 : Understanding Motion In One Dimension

Part of competing in a triathlon involves swimming in the open water. Suppose a woman competing swims at a speed of in still water and needs to swim . On the day of this particular race, there is an opposing current of going directly against the swimmer. How long does it take for her to finish the swim?

Possible Answers:

Correct answer:

Explanation:

The woman needs to swim , or . She normally swims at , but has a current opposing her. The effect will make her relative velocity equal to her normal velocity, minus the current against her.

We know that velocity is a change in distance divided by a change in time. Now that we have her relative velocity and the distance traveled, we can isolate the time variable and solve for her time.

Example Question #5 : Motion And Mechanics

Suppose a recreational biker averages on a twenty-mile ride, equal to . A professional biker has an average speed of . The professional happens to be riding on the same path, but started behind the recreational biker. The two are both headed for the same destination. Who would reach the end of the path first, and how far behind would the other biker be?

Possible Answers:

The professional finishes first and the other biker is behind

The recreational finishes first and the other biker is behind

The recreational finishes first and the other biker is behind

The professional finishes first and the other biker is behind

Both bikers reach destination at same time

Correct answer:

The professional finishes first and the other biker is behind

Explanation:

To solve this problem we can simply examine each biker separately and see how long it would take them to reach the destination. Let's begin with the recreational biker. The recreational biker needs to ride at . Using the definition of velocity, we can find his final time.

The professional has a distance of , plus the that he's behind.

We know that the velocity of the professional biker is . Using this velocity and his total distance, we can find the time that it takes him to reach the end of the path.

The time of the professional biker is less than that of the recreational biker, meaning that the professional will finish first. Now we need to find the distance between the two bikers at this point. Use the recreational biker's velocity and the time difference between the two bikers to solve for the distance that the recreational biker has left on the path.

Example Question #9 : Motion And Mechanics

Jenny throws a ball directly up in the air. She notices that it changes direction after approximately 3 seconds. What was the initial velocity of the ball?

Possible Answers:

Correct answer:

Explanation:

The ball will travel upwards to the highest point, then change direction and travel downwards. Remember that the velocity in at the highest point is equal to zero. We can use the following equation and our known data to solve for the initial velocity.

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